ONLY f, fi, fii3. Choose a country and research population data in order to fill out the table below
INIDAa. Copy the population numbers counted each five years, as shown in the data base, for
the years from 1950 to 2000. Add a column, t, measuring years since 1945.
Year |
t |
population |
1950 |
5 |
376,325,200 |
1955 |
5 |
409,880,595 |
1960 |
5 |
450,547,679 |
1965 |
5 |
499,123,324 |
1970 |
5 |
555,189,792 |
1975 |
5 |
623,102,897 |
1980 |
5 |
698,952,844 |
1985 |
5 |
784,360,008 |
1990 |
5 |
873,277,798 |
1995 |
5 |
963,922,588 |
2000 |
5 |
1,056,575,549 |
b. What is the country you selected? In what part of the world is it? What is the magnitude
of its population numbers? (100,000’s, millions, hundred millions, billions?) Is it growing or
shrinking in population size?
c. Enter years since 1945 and your population numbers into your graphing calculator.
Create a scatterplot of the data. Is the data growing or shrinking? Does it appear to be a
linear pattern or non-linear? Explain your conclusions.
d. Use your calculator to fit a linear model to the population size.
i. Write the equation of the linear regression and superimpose its graph on your scatterplot.
ii. Use TI-Connect to copy the scatterplot onto your write-up, or just draw a sketch of it.
iii. How well does the linear model fit your data?
iv. What is the vertical intercept of the regression model? What does it mean in the context
of the population?
v. What is the slope of the regression model? What does it mean in the context of the
population?
vi. Use the model to predict the population size in the year you were born. Also, use the
model to predict the population size in the year 2007.
e. Next fit an exponential model to your population data.
i. Write the equation of the exponential regression and superimpose its graph on your
scatterplot.
ii. How well does the exponential model fit your data? By looking at the graphs, does it
appear that the exponential model fits better than the linear model?
f. Next fit a power function to your population data.
i. Write the equation of the power regression and superimpose its graph on your
scatterplot.
ii. How well does the power model fit your data? By looking at the graphs, which of the
three models seems to fit the best?
g. Find the linear correlation coefficient for each model and compare them to determine
which model fits the data best.
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